lab6

Task 1

Working Directory

getwd()

## [1] "/home/joshua/Desktop/MainFolder/OuClasses/Spring 2023/Applied Statistical Methods/FALL224753wise0046/LABS/LAB6"

Task 2

Plot 4 normal curves (standard deviations)

layout(matrix(1:4,nr=2,nc=2))
curve(dnorm(x, mean=10,sd=4),xlim=c(10-3*4,10+3*4))
curve(dnorm(x, mean=10,sd=2),xlim=c(10-3*2,10+3*2))
curve(dnorm(x, mean=5,sd=10),xlim=c(5-3*10,5+3*10))
curve(dnorm(x, mean=5,sd=0.5),xlim=c(5-3*0.5,5+3*0.5))

Plot Regions and Probabilities (pnorm)

curve(dnorm(x, mean=0,sd=1),xlim=c(0-3,0+3))
xcurve <- seq(2, 3, length=1000)
ycurve <- dnorm(xcurve, 0, 1)
polygon(c(2, xcurve, 3), c(0,ycurve,0), col="Red")
area <- 1-pnorm(2,0,1)
area <- round(area,4)
text(5,0.2, paste0("Area= ",area))

curve(dnorm(x, mean=4,sd=2),xlim=c(4-3*2,4+3*2))
xcurve <- seq(1, 5, length=1000)
ycurve <- dnorm(xcurve, 4, 2)
polygon(c(1, xcurve, 5), c(0,ycurve,0), col="Red")
area <- pnorm(5,4,2)-pnorm(1,4,2)
area <- round(area,4)
text(8,0.2, paste0("Area= ",area))

curve(dnorm(x, mean=10,sd=4),xlim=c(10-3*4,10+3*4))
xcurve <- seq(10-3*4, 10, length=1000)
ycurve <- dnorm(xcurve, 10, 4)
polygon(c(10-3*4, xcurve, 10), c(0,ycurve,0), col="Red")
area <- pnorm(10,10,4)
area <- round(area,4)
text(5,0.2, paste0("Area= ",area))

curve(dnorm(x, mean=-2,sd=0.5),xlim=c(-2-3*0.5,-2+3*0.5))
xcurve <- seq(-3, -2, length=1000)
ycurve <- dnorm(xcurve, -2, 0.5)
polygon(c(-3, xcurve, -2), c(0,ycurve,0), col="Red")
area <- pnorm(-2,-2,0.5)-pnorm(-3,-2,0.5)
area <- round(area,4)
text(5,0.2, paste0("Area= ",area))

Task 3

Three Gamma Plots

curve(dgamma(x,shape=1,scale=1),xlim=c(0,10),ylim=c(0,1),col="Red",lwd=2,
ylab="Gamma density", main="Beta=1")
curve(dgamma(x,shape=3,scale=1),xlim=c(0,10),ylim=c(0,1),add=TRUE,lwd=2)
curve(dgamma(x,shape=5,scale=1),xlim=c(0,10),ylim=c(0,1),add=TRUE, col="Blue",lwd=2)

Plot Regions and Probabilities (pgamma)

curve(dgamma(x,shape=3,scale=2),xlim=c(0,10),ylim=c(0,0.2),col="Red",lwd=2,
ylab="Gamma density", main="Beta=2")
xcurve <- seq(2, 5, length=1000)
ycurve <- dgamma(xcurve,shape=3,scale=2)
polygon(c(2, xcurve, 5), c(0,ycurve,0), col="Red")
area <- pgamma(5,shape=3,scale=2)-pgamma(2,shape=3,scale=2)
area <- round(area,4)
text(5,0.2, paste0("Area= ",area))

curve(dgamma(x,shape=6,scale=3),xlim=c(0,10),ylim=c(0,0.1),col="Red",lwd=2,
ylab="Gamma density", main="Beta=3")
xcurve <- seq(1, 4, length=1000)
ycurve <- dgamma(xcurve,shape=6,scale=3)
polygon(c(1, xcurve, 4), c(0,ycurve,0), col="Red")
area <- pgamma(4,shape=6,scale=3)-pgamma(1,shape=6,scale=3)
area <- round(area,4)
text(5,0.2, paste0("Area= ",area))

curve(dgamma(x,shape=2,scale=4),xlim=c(0,10),ylim=c(0,0.2),col="Red",lwd=2,
ylab="Gamma density", main="Beta=4")
xcurve <- seq(3, 6, length=1000)
ycurve <- dgamma(xcurve,shape=2,scale=4)
polygon(c(3, xcurve, 6), c(0,ycurve,0), col="Red")
area <- pgamma(6,shape=2,scale=4)-pgamma(3,shape=2,scale=4)
area <- round(area,4)
text(5,0.2, paste0("Area= ",area))

Task 4

Plot 4 (chi-squares)

curve(dchisq(x,df=1),xlim=c(0,10),ylim=c(0,1),col="Red",lwd=2,
ylab="Chisq density", main="df=1,2,4,20")
curve(dchisq(x,df=2),xlim=c(0,10),ylim=c(0,1),col="Blue",lwd=2,
ylab="Chisq density",add=TRUE)
curve(dchisq(x,df=4),xlim=c(0,10),ylim=c(0,1),col="Black",lwd=2,
ylab="Chisq density",add=TRUE)
curve(dchisq(x,df=20),xlim=c(0,10),ylim=c(0,1),col="Green",lwd=2,
ylab="Chisq density",add=TRUE)

Plot Regions and Probabilities (chi-squares)

curve(dchisq(x,df=2),xlim=c(0,10),ylim=c(0,1),col="Red",lwd=2,
ylab="Chisq density", main="df=2")
xcurve <- seq(2, 4, length=1000)
ycurve <- dchisq(xcurve,2)
polygon(c(2, xcurve, 4), c(0,ycurve,0), col="Red")
area <- dchisq(4,2)-dchisq(2,2)
area <- round(area,4)
text(5,0.2, paste0("Area= ",area))

curve(dchisq(x,df=3),xlim=c(0,10),ylim=c(0,1),col="Red",lwd=2,
ylab="Chisq density", main="df=3")
xcurve <- seq(3, 5, length=1000)
ycurve <- dchisq(xcurve,3)
polygon(c(3, xcurve, 5), c(0,ycurve,0), col="Red")
area <- dchisq(5,3)-dchisq(3,3)
area <- round(area,4)
text(5,0.2, paste0("Area= ",area))

curve(dchisq(x,df=20),xlim=c(5,26),ylim=c(0,1),col="Red",lwd=2,
ylab="Chisq density", main="df=20")
xcurve <- seq(10, 21, length=1000)
ycurve <- dchisq(xcurve,20)
polygon(c(10, xcurve, 21), c(0,ycurve,0), col="Red")
area <- dchisq(21,20)-dchisq(10,20)
area <- round(area,4)
text(10,0.2, paste0("Area= ",area))

Task 5

Plot 4 (Weibull)

layout(matrix(1:4,nr=2,nc=2))
curve(dweibull(x, shape=8, scale=2),xlim=c(0,10))
curve(dweibull(x, shape=5, scale=5),xlim=c(0,10))
curve(dweibull(x, shape=2, scale=8),xlim=c(0,10))
curve(dweibull(x, shape=3, scale=9),xlim=c(0,10))

Plot Regions and Probabilities (Weibull)

curve(dweibull(x, shape=5, scale=5),xlim=c(0,10), ylab="dwibull density", main="Beta=3")
xcurve <- seq(4, 7, length=1000)
ycurve <- dweibull(xcurve,shape=5,scale=5)
polygon(c(4, xcurve, 7), c(0,ycurve,0), col="Red")
area <- pweibull(7, shape=5, scale=5)-pweibull(4, shape=5, scale=5)
area <- round(area,4)
text(10,0.2, paste0("Area= ",area))

curve(dweibull(x, shape=8, scale=2),xlim=c(0,10), ylab="dwibull density", main="Beta=3")
xcurve <- seq(1, 2, length=1000)
ycurve <- dweibull(xcurve,shape=8,scale=2)
polygon(c(1, xcurve, 2), c(0,ycurve,0), col="Red")
area <- pweibull(2, shape=8, scale=2)-pweibull(1, shape=8, scale=2)
area <- round(area,4)
text(10,0.2, paste0("Area= ",area))

curve(dweibull(x, shape=2, scale=8),xlim=c(0,10), ylab="dwibull density", main="Beta=3")
xcurve <- seq(1, 4, length=1000)
ycurve <- dweibull(xcurve,shape=2,scale=8)
polygon(c(1, xcurve, 4), c(0,ycurve,0), col="Red")
area <- pweibull(4, shape=2, scale=8)-pweibull(1, shape=2, scale=8)
area <- round(area,4)
text(10,0.2, paste0("Area= ",area))

Task 6

Plot 4 (Beta distribution)

layout(matrix(1:4,nr=2,nc=2))
curve(dbeta(x,13,20),xlim=c(0,10))
curve(dbeta(x,20,13),xlim=c(0,10))
curve(dbeta(x,2,2),xlim=c(0,10))
curve(dbeta(x,5,1),xlim=c(0,10))

Plot Regions and Probabilities (Beta distribution)

curve(dbeta(x,13,20),xlim=c(0,10))
xcurve <- seq(0, 0.75, length=1000)
ycurve <- dbeta(xcurve,13,20)
polygon(c(0, xcurve, 0.75), c(0,ycurve,0), col="Red")
area <- pbeta(0.75,13,20)-pbeta(0,13,20)
area <- round(area,4)
text(8,0.2, paste0("Area= ",area))

curve(dbeta(x,2,2),xlim=c(0,10))
xcurve <- seq(0, 0.25, length=1000)
ycurve <- dbeta(xcurve,2,2)
polygon(c(0, xcurve, 0.25), c(0,ycurve,0), col="Red")
area <- pbeta(0.25,2,2)-pbeta(0,2,2)
area <- round(area,4)
text(8,0.2, paste0("Area= ",area))

curve(dbeta(x,5,1),xlim=c(0,10))
xcurve <- seq(0, 1, length=1000)
ycurve <- dbeta(xcurve,5,1)
polygon(c(0, xcurve, 1), c(0,ycurve,0), col="Red")
area <- pbeta(1,5,1)-pbeta(0,5,1)
area <- round(area,4)
text(8,0.2, paste0("Area= ",area))

Task 7

notmyncurve()

notmyncurve = function(a, mu, sigma){
  curve(dnorm(x,mean=mu,sd=sigma), xlim = c(mu-3*sigma, mu + 3*sigma))
  xcurve <- seq(mu-3*sigma, a, length=1000)
  ycurve <- dnorm(xcurve, mu, sigma)
  polygon(c(mu-3*sigma, xcurve, a), c(0,ycurve,0), col="Red")
  area <- pnorm(a,mu,sigma)
  area <- round(area,4)
  text(mu+2*sigma,0.2, paste0("Area= ",area))
}
notmyncurve(12, 10, 2)

myncurve()

BestRPackage::myncurve(a=9,mu=10,sigma=2)